相关论文: Continuous and Twisted L_infinity Morphisms
We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.
We define unbounded twisted complexes and bicomplexes generalising the notion of a (bounded) twisted complex over a DG category [BK90]. These need to be considered relative to another DG category $B$ admitting countable direct sums and…
We show that an $L_\infty$-algebra can be extended to a graded Hopf algebra with a codifferential. Then we twist this extended $L_\infty$-algebra with a Drinfel'd twist, simultaneously twisting its modules. Taking the $L_\infty$-algebra as…
Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…
The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…
The notion of a matched pair of Lie algebras was introduced in the study of Lie bialgebras and Poisson-Lie groups. In this paper, we introduce representations and cohomology of a matched pair of Lie algebras. We show that there is a…
We show that the mapping cone of a morphism of differential graded Lie algebras $\chi\colon L\to M$ can be canonically endowed with an $L_\infty$-algebra structure which at the same time lifts the Lie algebra structure on $L$ and the usual…
We define the notion of action of an L-infinity algebra $g$ on a graded manifold $M$, and show that such an action corresponds to a homological vector field on $g[1] \times M$ of a specific form. This generalizes the correspondence between…
We study noncommutative deformations of Yang-Mills theories and show that these theories admit a infinite, continuous family of twisted star-gauge invariances. This family interpolates continuously between star-gauge and twisted gauge…
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \sigma-finite morphism between difference curves are…
We study the relationship between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, which leads to a new approach to the infinitesimal description of multiplicative 2-forms and to the integration of twisted Dirac…
The purpose of this paper is to provide a new account of multiplicity for finite morphisms between smooth projective varieties. Traditionally, this has been defined using commutative algebra in terms of the length of integral ring…
This is a brief overview of a few selected chapters on automorphism groups of affine varieties. It includes some open questions.
The purpose of this paper is to consider when two maximal subalgebras of a finite-dimensional solvable Lie algebra $L$ are conjugate, and to investigate their intersection.
It has been proposed that the Poincare and some other symmetries of noncommutative field theories should be twisted. Here we extend this idea to gauge transformations and find that twisted gauge symmetries close for arbitrary gauge group.…
We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint…
We introduce perfect resolving algebras and study their fundamental properties. These algebras are basic for our theory of differential graded schemes, as they give rise to affine differential graded schemes. We also introduce etale…
We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
We study formal deformations of multiplication in an operad. This closely resembles Gerstenhaber's deformation theory for associative algebras. However, this applies to various algebras of Loday-type and their twisted analogs. We explicitly…